How does synchrony of tree growth vary across regional/elevation gradients? Prediction: higher synchrony in lower latitude and lower elevation (drier) populations (SIASH, dendrochronological principles)
Within populations is intraspecific synchrony greater than interspecific synchrony? Between specific species pairs? With increasing distance? Prediction: higher synchrony among intraspecific pairs, potentially higher synchrony between pine pairs versus pine-fir pairs (successional stages), and lower synchrony with increasing distance
How has synchrony changed through time? Are changes more dramatic in certain populations? Is increased or decreased synchrony associated with certain environmental variables? Prediction: synchrony has increased with time, increased synchrony associated with drier, more variable time windows, changes are more pronounced in xeric populations.
Synchrony is explored here through residual correlations betweeen trees from multivariate models of tree growth.
We calculated the correlation between series of tree ring growth for all unique pairs of individuals within competitive neighborhoods.
## # A tibble: 10 x 6
## # Groups: spp1, spp2 [10]
## spp1 spp2 pair med mean sd
## <chr> <chr> <chr> <dbl> <dbl> <dbl>
## 1 ac ac ac-ac 0.442 0.442 0.227
## 2 ac pj ac-pj 0.301 0.287 0.225
## 3 ac pl ac-pl 0.298 0.292 0.217
## 4 ac pp ac-pp 0.125 0.132 0.191
## 5 pj pj pj-pj 0.281 0.288 0.210
## 6 pj pl pj-pl 0.206 0.236 0.222
## 7 pj pp pj-pp 0.555 0.486 0.215
## 8 pl pl pl-pl 0.516 0.459 0.263
## 9 pl pp pl-pp 0.347 0.330 0.223
## 10 pp pp pp-pp 0.357 0.320 0.286
We wanted to data the relationship between the pairwise correlations and distance, size ratios, species-pairs, and locations of all of the trees. We built hierarchical mixed models with the pairwise correlations as a responses (normal truncated response (-1,1)).
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: pearson_r | trunc(lb = -1.001, ub = 1.001) ~ dist + sizeratio + (1 | pair/Region:hilo) + (1 | Region:hilo/Neighborhood.x)
## Data: alldata (Number of observations: 918)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Group-Level Effects:
## ~pair (Number of levels: 10)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.08 0.03 0.03 0.16 1.00 1578 2074
##
## ~pair:Region:hilo (Number of levels: 45)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.06 0.02 0.03 0.10 1.00 1282 2161
##
## ~Region:hilo (Number of levels: 7)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.11 0.06 0.01 0.27 1.00 770 774
##
## ~Region:hilo:Neighborhood.x (Number of levels: 21)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.11 0.03 0.07 0.17 1.00 1348 2365
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.33 0.06 0.21 0.45 1.00 2095 2304
## dist -0.02 0.01 -0.04 -0.01 1.00 7052 3113
## sizeratio -0.02 0.01 -0.03 -0.00 1.00 7702 2772
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.18 0.00 0.17 0.19 1.00 6828 2796
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
| pair | spp_mean | .lower | .upper | .width |
|---|---|---|---|---|
| ac-ac | 0.4299308 | 0.3125735 | 0.5504589 | 0.95 |
| ac-pj | 0.2895771 | 0.1742056 | 0.4112417 | 0.95 |
| ac-pl | 0.3347854 | 0.2199933 | 0.4538857 | 0.95 |
| ac-pp | 0.2608846 | 0.1022052 | 0.4055108 | 0.95 |
| pj-pj | 0.3029418 | 0.1848707 | 0.4216935 | 0.95 |
| pj-pl | 0.2968228 | 0.1804234 | 0.4173941 | 0.95 |
| pj-pp | 0.3483507 | 0.2020051 | 0.5036207 | 0.95 |
| pl-pl | 0.4172842 | 0.2942625 | 0.5467758 | 0.95 |
| pl-pp | 0.2979674 | 0.1473677 | 0.4423177 | 0.95 |
| pp-pp | 0.3071704 | 0.1441655 | 0.4588228 | 0.95 |
| pair | .value | .lower | .upper | .width |
|---|---|---|---|---|
| ac-ac | 0.4387708 | 0.3226548 | 0.5563286 | 0.95 |
| ac-pj | 0.2990584 | 0.1841286 | 0.4216713 | 0.95 |
| ac-pl | 0.3443731 | 0.2280349 | 0.4630147 | 0.95 |
| ac-pp | 0.2702899 | 0.1119400 | 0.4161674 | 0.95 |
| pj-pj | 0.3128785 | 0.1941582 | 0.4305085 | 0.95 |
| pj-pl | 0.3063874 | 0.1897233 | 0.4256633 | 0.95 |
| pj-pp | 0.3576522 | 0.2112857 | 0.5111900 | 0.95 |
| pl-pl | 0.4263587 | 0.3045571 | 0.5526348 | 0.95 |
| pl-pp | 0.3071737 | 0.1561637 | 0.4512196 | 0.95 |
| pp-pp | 0.3168582 | 0.1515273 | 0.4684363 | 0.95 |
| Region | hilo | mean | mean.lower | mean.upper | .width |
|---|---|---|---|---|---|
| Mammoth | high | 0.4261706 | 0.2779546 | 0.5845998 | 0.95 |
| San.Jac | high | 0.3211825 | 0.1945011 | 0.4468180 | 0.95 |
| San.Jac | low | 0.3735080 | 0.2482383 | 0.5118101 | 0.95 |
| SEKI | high | 0.2309234 | 0.0798710 | 0.3788555 | 0.95 |
| SEKI | low | 0.2679966 | 0.1321744 | 0.3985046 | 0.95 |
| SENF | high | 0.3247677 | 0.1904712 | 0.4463505 | 0.95 |
| SENF | low | 0.3533152 | 0.2198490 | 0.4840910 | 0.95 |
| Region | hilo | .value | .lower | .upper | .width | Site | total_ppt_mm_fn1 | mean_temp_C_fn1 | spei12_fn1 | total_ppt_mm_fn2 | mean_temp_C_fn2 | spei12_fn2 | ppt_cv | temp_cv | pca1 | pca2 | site |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Mammoth | high | 0.4361825 | 0.2864044 | 0.5895564 | 0.95 | sl | 662.8551 | 4.976681 | 0.0056064 | 243.8779 | 0.8644964 | 0.9924980 | 0.3679204 | 0.1737094 | 0.3994751 | 1.8371042 | Mammoth_high |
| San.Jac | high | 0.3307396 | 0.2043351 | 0.4566170 | 0.95 | bm | 726.5933 | 8.650685 | 0.0067780 | 276.3013 | 0.8554435 | 0.9986706 | 0.3802695 | 0.0988874 | -0.7095735 | 0.2417688 | San.Jac_high |
| San.Jac | low | 0.3827795 | 0.2584360 | 0.5192507 | 0.95 | sp | 685.1577 | 11.096213 | 0.0069195 | 260.5055 | 0.8059019 | 0.9987380 | 0.3802125 | 0.0726285 | -1.7676989 | -0.5002259 | San.Jac_low |
| SEKI | high | 0.2406349 | 0.0888628 | 0.3894296 | 0.95 | pr | 1113.5588 | 6.734041 | 0.0066853 | 397.6937 | 0.9431085 | 0.9933142 | 0.3571376 | 0.1400509 | 1.4720001 | -0.5289892 | SEKI_high |
| SEKI | low | 0.2776652 | 0.1420893 | 0.4083442 | 0.95 | cm | 1081.8940 | 8.423422 | 0.0062335 | 385.8646 | 0.9270428 | 0.9923128 | 0.3566565 | 0.1100554 | 0.7294427 | -1.0299620 | SEKI_low |
| SENF | high | 0.3345610 | 0.1997250 | 0.4558551 | 0.95 | pp | 896.6415 | 7.340703 | 0.0070685 | 325.4096 | 0.8139782 | 0.9953052 | 0.3629206 | 0.1108856 | 0.4212430 | 0.0752121 | SENF_high |
| SENF | low | 0.3625846 | 0.2289590 | 0.4917346 | 0.95 | lc | 792.3074 | 8.884342 | 0.0067976 | 288.6899 | 0.8171269 | 0.9965620 | 0.3643661 | 0.0919738 | -0.5448884 | -0.0949081 | SENF_low |
##
## Call:
## lm(formula = data$mean ~ data$total_ppt_mm_fn1)
##
## Residuals:
## 1 2 3 4 5 6 7
## 0.037445 -0.047092 -0.008061 -0.013192 0.013722 0.011054 0.006125
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.014e-01 5.548e-02 10.840 0.000116 ***
## data$total_ppt_mm_fn1 -3.209e-04 6.388e-05 -5.022 0.004027 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02901 on 5 degrees of freedom
## Multiple R-squared: 0.8346, Adjusted R-squared: 0.8015
## F-statistic: 25.22 on 1 and 5 DF, p-value: 0.004027
##
## Call:
## lm(formula = site_summ$.value ~ site_summ$total_ppt_mm_fn1)
##
## Residuals:
## 1 2 3 4 5 6 7
## 0.037896 -0.047113 -0.008357 -0.013163 0.013716 0.011223 0.005799
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.108e-01 5.574e-02 10.958 0.00011 ***
## site_summ$total_ppt_mm_fn1 -3.206e-04 6.419e-05 -4.995 0.00412 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02914 on 5 degrees of freedom
## Multiple R-squared: 0.833, Adjusted R-squared: 0.7996
## F-statistic: 24.95 on 1 and 5 DF, p-value: 0.004124
##
## Call:
## lm(formula = .value ~ total_ppt_mm_fn1 * pair, data = site_sp_summ)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.06631 -0.01452 0.00000 0.01797 0.07175
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.369e-01 7.817e-02 8.148 1.25e-08 ***
## total_ppt_mm_fn1 -2.201e-04 9.001e-05 -2.446 0.021544 *
## pairac-pj -2.856e-01 1.175e-01 -2.431 0.022264 *
## pairac-pl -2.268e-01 1.195e-01 -1.897 0.068934 .
## pairac-pp -5.076e-01 1.533e-01 -3.310 0.002737 **
## pairpj-pj -3.663e-01 1.105e-01 -3.314 0.002712 **
## pairpj-pl -3.453e-01 1.195e-01 -2.888 0.007702 **
## pairpj-pp -2.880e-01 1.533e-01 -1.879 0.071568 .
## pairpl-pl -2.163e-01 1.195e-01 -1.810 0.081885 .
## pairpl-pp -3.976e-01 1.533e-01 -2.593 0.015420 *
## pairpp-pp -1.876e-01 4.618e-02 -4.063 0.000397 ***
## total_ppt_mm_fn1:pairac-pj 1.540e-04 1.331e-04 1.158 0.257549
## total_ppt_mm_fn1:pairac-pl 1.458e-04 1.351e-04 1.079 0.290339
## total_ppt_mm_fn1:pairac-pp 3.511e-04 1.712e-04 2.050 0.050553 .
## total_ppt_mm_fn1:pairpj-pj 2.652e-04 1.273e-04 2.083 0.047192 *
## total_ppt_mm_fn1:pairpj-pl 2.304e-04 1.351e-04 1.706 0.099957 .
## total_ppt_mm_fn1:pairpj-pp 2.380e-04 1.712e-04 1.390 0.176314
## total_ppt_mm_fn1:pairpl-pl 2.403e-04 1.351e-04 1.779 0.086863 .
## total_ppt_mm_fn1:pairpl-pp 2.846e-04 1.712e-04 1.662 0.108523
## total_ppt_mm_fn1:pairpp-pp NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04087 on 26 degrees of freedom
## Multiple R-squared: 0.8265, Adjusted R-squared: 0.7063
## F-statistic: 6.879 on 18 and 26 DF, p-value: 6.499e-06
We calculated pearson correlations between pairs of individuals within neighborhoods for 30 year time blocks with a 10 year lag to measure synchrony through time. Trends were analyzed for data summarized for species-pairs at the neighborhood level. Note this is measuring within population synchrony (in contrast to Shestakova spatial synchrony).
I wanted to explore fitting a spline model to look at nonlinear changes in synchrony over time for different species-pairs and at different sites.
## pearson_r ~ s(decade)
## pearson_r ~ pair + s(decade, by = pair)
## pearson_r ~ Site.x + s(decade, by = Site.x)
Model selection supported SPEI as the best predictor for synchrony. I included both mean and sd in one model although the variables are correlatedd (~.3). I did not do multiple regression because of multicollinearity.
## pearson_r | trunc(lb = -1.001, ub = 1.001) ~ total_ppt_mm_cv + (total_ppt_mm_cv | Site.x) + (1 | Site.x:pair)